Row Stochastic Matrices Similar to Doubly Stochastic Matrices

The problem of determining which row stochastic n-by-n matrices are similar to doubly stochastic matrices is considered. That not all are is indicated by example, and an abstract characterization as well as various explicit sufficient conditions are given. For example, if a row stochastic matrix has no entry smaller than (n+1)^-1 it is similar to a doubly stochastic matrix.

Relaxing the nonnegativity requirement, the real matrices which are similar to real matrices with row and column sums one are then characterized, and it is observed that all row stochastic matrices have this property. Some remarks are then made on the nonnegative eigenvalue problem with respect to i) a necessary trace inequality and ii) removing zeroes from the spectrum.     

Two-Stage Stochastic Runge-Kutta Methods for Stochastic Differential Equations

In this paper we discuss two-stage diagonally implicit stochastic Runge-Kutta methods with strong order 1.0 for strong solutions of Stratonovich stochastic differential equations. Five stochastic Runge-Kutta methods are presented in this paper. They are an explicit method with a large MS-stability region, a semi-implicit method with minimum principal error coefficients, a semi-implicit method with a large MS-stability region, an implicit method with minimum principal error coefficients and another implicit method. We also consider composite stochastic Runge-Kutta methods which are the combination of semi-implicit Runge-Kutta methods and implicit Runge-Kutta methods. Two composite methods are presented in this paper. Numerical results are reported to compare the convergence properties and stability properties of these stochastic Runge-Kutta methods.     

具有随机加速度的随机运动的存在性

讨论了随机加速度为位移的给定函数的随机运动的存在性(即R上的随机微分方程弱解的存在性),给出并证明了具有随机加速度的随机运动存在的几个充分性条件.     

Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming

We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the two problems is shown under some moderate conditions, and the monotonicity of the two-stage stochastic variational inequality is discussed under additional conditions. We provide a discretization scheme with convergence results and employ the progressive hedging method with double parameterization to solve the discretized stochastic variational inequality. As an application, we show how the water resources management problem under uncertainty can be transformed from a two-stage stochastic programming problem to a two-stage stochastic variational inequality, and how to solve it, using the discretization scheme and the progressive hedging method with double parameterization.

     

Stochastic backtrackings

A particle moves with constant velocity in the positive direction. It is also subject to randomly occuring instantaneous negative displacements called backtrackings. The magnitudes of these displacements are independent and identically distributed random variables, and it is assumed that the net velocity of the pa?ticle is still positive. The backtrackings are registered but the times of their occurence are not. The resulting collection of overlapping intervals on the real line is studied as a stochastic process evolving in space. A fairly simple Markovian representation is derived and the stationary distribution obtained. Intimate connections with certain linear immigration-birth-death processes are exhibited. Some comments are made concerning estimation and sampling procedures and the identifiability of the displacement distribution from limited information.     

Stochastic Rumours

The superficial similarity between rumours and epidemics breaksdown on closer scrutiny; a feature peculiar to the rumour-spreadingsituation leads to striking qualitative differences in the behaviourof the two phenomena whether one uses a stochastic model orthe associated deterministic model. A preliminary account isgiven here of a new procedure, "the principle of the diffusionof arbitrary constants", which can be used to study the varianceof the fluctuations of the sample trajectory in the stochasticmodel about the unique trajectory in the associated deterministicapproximation. Numerical evidence (based on Monte Carlo andother calculations) is given to illustrate the effectivenessof the "principle" in the present application.     

Stochastic games

Stochastic Games have a value.